%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP401-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:28:47 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 28 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 18 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(associativity_of_multiply,axiom,
! [VAR_0,VAR_1,VAR_2] : multiply(multiply(VAR_0,VAR_1),VAR_2) = multiply(VAR_0,multiply(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_multiply) ).
cnf(c_1,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(clausify,[status(thm)],[associativity_of_multiply]) ).
fof(right_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_2,VAR_1) ),
file('theBenchmark.p',right_cancellation) ).
cnf(c_2,plain,
( A = C
| multiply(A,B) != multiply(C,B) ),
inference(clausify,[status(thm)],[right_cancellation]) ).
fof(left_cancellation,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = VAR_2
| multiply(VAR_0,VAR_1) != multiply(VAR_0,VAR_2) ),
file('theBenchmark.p',left_cancellation) ).
cnf(c_3,plain,
( B = C
| multiply(A,B) != multiply(A,C) ),
inference(clausify,[status(thm)],[left_cancellation]) ).
fof(commutator,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = multiply(VAR_1,multiply(VAR_0,commutator(VAR_0,VAR_1))),
file('theBenchmark.p',commutator) ).
cnf(c_4,plain,
multiply(A,B) = multiply(B,multiply(A,commutator(A,B))),
inference(clausify,[status(thm)],[commutator]) ).
cnf(c_5,plain,
multiply(A,multiply(B,commutator(B,A))) = multiply(B,A),
inference(copy,[status(thm)],[c_4]) ).
fof(commutator_distributes_over_product,axiom,
! [VAR_0,VAR_1,VAR_2] : commutator(multiply(VAR_0,VAR_1),VAR_2) = multiply(commutator(VAR_0,VAR_2),commutator(VAR_1,VAR_2)),
file('theBenchmark.p',commutator_distributes_over_product) ).
cnf(c_6,plain,
commutator(multiply(A,B),C) = multiply(commutator(A,C),commutator(B,C)),
inference(clausify,[status(thm)],[commutator_distributes_over_product]) ).
fof(prove_nilpotency,axiom,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
file('theBenchmark.p',prove_nilpotency) ).
cnf(c_7,plain,
multiply(commutator(a,b),c) != multiply(c,commutator(a,b)),
inference(clausify,[status(thm)],[prove_nilpotency]) ).
cnf(c_8,plain,
( multiply(A,B) = D
| multiply(A,multiply(B,C)) != multiply(D,C) ),
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_225,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(multiply(A,commutator(A,B)),C)),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_226,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(multiply(A,commutator(A,B)),C)),
inference(paramod,[status(thm)],[c_1,c_225]) ).
cnf(c_227,plain,
multiply(A,multiply(B,C)) = multiply(B,multiply(A,multiply(commutator(A,B),C))),
inference(paramod,[status(thm)],[c_1,c_226]) ).
cnf(c_11,plain,
multiply(A,multiply(B,multiply(commutator(B,A),C))) = multiply(B,multiply(A,C)),
inference(copy,[status(thm)],[c_227]) ).
cnf(c_228,plain,
multiply(A,multiply(B,multiply(C,commutator(multiply(B,C),A)))) = multiply(multiply(B,C),A),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_229,plain,
multiply(A,multiply(B,multiply(C,multiply(commutator(B,A),commutator(C,A))))) = multiply(multiply(B,C),A),
inference(paramod,[status(thm)],[c_6,c_228]) ).
cnf(c_13,plain,
multiply(A,multiply(B,multiply(C,multiply(commutator(B,A),commutator(C,A))))) = multiply(B,multiply(C,A)),
inference(paramod,[status(thm)],[c_1,c_229]) ).
cnf(c_18,plain,
multiply(A,multiply(commutator(a,b),c)) != multiply(A,multiply(c,commutator(a,b))),
inference(resolve,[status(thm)],[c_3,c_7]) ).
cnf(c_26,plain,
multiply(A,multiply(B,multiply(commutator(a,b),c))) != multiply(A,multiply(B,multiply(c,commutator(a,b)))),
inference(resolve,[status(thm)],[c_3,c_18]) ).
cnf(c_230,plain,
multiply(a,multiply(b,c)) != multiply(b,multiply(a,multiply(c,commutator(a,b)))),
inference(paramod,[status(thm)],[c_11,c_26]) ).
cnf(c_144,plain,
multiply(b,multiply(a,multiply(c,commutator(a,b)))) != multiply(a,multiply(b,c)),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_231,plain,
multiply(b,multiply(multiply(a,multiply(c,commutator(a,b))),A)) != multiply(multiply(a,multiply(b,c)),A),
inference(resolve,[status(thm)],[c_8,c_144]) ).
cnf(c_232,plain,
multiply(b,multiply(a,multiply(multiply(c,commutator(a,b)),A))) != multiply(multiply(a,multiply(b,c)),A),
inference(paramod,[status(thm)],[c_1,c_231]) ).
cnf(c_233,plain,
multiply(b,multiply(a,multiply(c,multiply(commutator(a,b),A)))) != multiply(multiply(a,multiply(b,c)),A),
inference(paramod,[status(thm)],[c_1,c_232]) ).
cnf(c_234,plain,
multiply(b,multiply(a,multiply(c,multiply(commutator(a,b),A)))) != multiply(a,multiply(multiply(b,c),A)),
inference(paramod,[status(thm)],[c_1,c_233]) ).
cnf(c_153,plain,
multiply(b,multiply(a,multiply(c,multiply(commutator(a,b),A)))) != multiply(a,multiply(b,multiply(c,A))),
inference(paramod,[status(thm)],[c_1,c_234]) ).
cnf(c_235,plain,
multiply(b,multiply(a,multiply(c,multiply(commutator(a,b),commutator(c,b))))) != multiply(a,multiply(c,b)),
inference(paramod,[status(thm)],[c_5,c_153]) ).
cnf(c_236,plain,
multiply(a,multiply(c,b)) != multiply(a,multiply(c,b)),
inference(paramod,[status(thm)],[c_13,c_235]) ).
cnf(c_224,plain,
$false,
inference(copy,[status(thm)],[c_236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP401-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 14:56:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 2674986 was started by sandbox on n016,
% 0.10/0.37 % Fri Sep 25 14:56:14 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.44
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.44
% 0.10/0.44 % Proof 1 at 0.03 (+ 0.02) seconds.
% 0.10/0.44 % Length of proof is 15.
% 0.10/0.44 % Level of proof is 5.
% 0.10/0.44 % Maximum clause weight is 19.000.
% 0.10/0.44 % Given clauses 36.
% 0.10/0.44
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------